This work explores new usages of experimental and analysis tools to study the relationship between the wave propagation and sound radiation in a structure with inhomogeneities. The focus of the research is to develop and test new and merged techniques. The analysis tools used in the research include: time domain analysis, k-space analysis, and wave speed tracking. With the time domain analysis, one can study the response of any synthetic excitation with only one set of experimental data. The k-space analysis provides insight into locating areas on a vibrating structure that radiate sound to the acoustic farfield. The wave speed tracking technique was developed to estimate the phase speed of propagating waves in a structure. In addition, the reflection coefficient of a boundary can be computed from the wave speed tracking results. The chirp signal, used in the experiments, provides a concentrated power signal which can excite every mode in the interested frequency range. In addition, the transient property of the chirp signal also provides information in the time domain. A very consistent experimental setup and a repeatable experimental procedure were designed and tested to minimize the errors caused by the setup or mishandling of the equipment;A plate equation with a spatially distributed stress was used to model a structure with inhomogeneities. The results of simulations show that the spatially distributed stress can change the amplitude and wavenumbers of the waves in the plate. A HY-80 steel beam with a T-bar welded to it was investigated experimentally with the proposed tools. The T-bar shows a significant contribution to the radiated sound power, and the existence of the T-bar decreases the phase speed of the propagating waves around the T-bar by 4% to 7%. The heat treatment did not have much influence on the sound radiation or wave phase speed change in this study. The experimental results have proven that the proposed techniques are very useful in the study of wave propagation and sound radiation for structures.